1. CHEMICAL CONCEPTS CE 370 – Lecture 3

2. Inorganic Chemistry Definitions Definitions Concentration Units Concentration Units Chemical Equilibria Chemical Equilibria pH and Alkalinity pH and Alkalinity

3. DEFINITIONS Atomic Weight: is the weight of an element when compared to Carbon (Carbon atomic weight is 12) Atomic Weight: is the weight of an element when compared to Carbon (Carbon atomic weight is 12) Valence: is the combining power of the element when compared to Hydrogen (Hydrogen has a combining power of 1) Valence: is the combining power of the element when compared to Hydrogen (Hydrogen has a combining power of 1) Equivalent Weight = Atomic Weight / Valence Equivalent Weight = Atomic Weight / Valence

4. DEFINITIONS Molecular weight : is the sum of the atomic weights of the combined elements Molecular weight : is the sum of the atomic weights of the combined elements Equivalent weight of a compound : is that weight of the compound which contains 1 gram atom of available hydrogen or its chemical equivalent. Equivalent weight of a compound : is that weight of the compound which contains 1 gram atom of available hydrogen or its chemical equivalent.

5. Concentration Units milligram per liter (mg / l) milligram per liter (mg / l) part per million (ppm) part per million (ppm) kilograms per million liters kilograms per million liters milliequivalents per liter = [(mg/l) / eq weight] milliequivalents per liter = [(mg/l) / eq weight]

6. Hydrogen Ion Concentration When pure water dissociates: H 2 O  H + + OH - H 2 O  H + + OH - concentration of H + ion is 10 -7 mole per liter concentration of H + ion is 10 -7 mole per liter concentration of OH - ion is 10 -7 mole per liter concentration of OH - ion is 10 -7 mole per liter Since H + concentration = OH - concentration, the water is neutral Since H + concentration = OH - concentration, the water is neutral

7. Acidic or Basic? pH = log ( 1 / [H + ] ) pH = log ( 1 / [H + ] ) When [H + ] concentration is 10 -7, then pH =7, which represents the neutral state. When [H + ] concentration is 10 -7, then pH =7, which represents the neutral state. If pH > 7, then it is basic If pH > 7, then it is basic If pH < 7, then it is acidic If pH < 7, then it is acidic Water ionization is represented by: Water ionization is represented by: [H + ][OH - ] = K w = 10 -14 [H + ][OH - ] = K w = 10 -14

8. Chemical Equilibria aA + bB  cC + dD aA + bB  cC + dD A and B are the reactants A and B are the reactants C and D are the products C and D are the products [C] c [D] d / [A] a [B] b = K [C] c [D] d / [A] a [B] b = K [ ] = molar concentration and K=equilibrium constant [ ] = molar concentration and K=equilibrium constant In Water Chemistry, In Water Chemistry, H 2 CO 3  H + + HCO 3 - H 2 CO 3  H + + HCO 3 - [H + ][HCO 3 - ] / [H 2 CO 3 ] = K 1 = 4.45  10 -7 @ 25  C} [H + ][HCO 3 - ] / [H 2 CO 3 ] = K 1 = 4.45  10 -7 @ 25  C} HCO 3 -  H + + CO 3 -2 HCO 3 -  H + + CO 3 -2 [H + ][CO 3 -2 ] / [HCO 3 ] = K 2 = 4.69  10 -11 @ 25  C} [H + ][CO 3 -2 ] / [HCO 3 ] = K 2 = 4.69  10 -11 @ 25  C} are very important equilibrium relationships are very important equilibrium relationships

9. CaCO 3  Ca +2 + CO 3 - (at pH = 10) CaCO 3  Ca +2 + CO 3 - (at pH = 10) [Ca +2 ][CO 3 - ] / [CaCO 3 ] = K [Ca +2 ][CO 3 - ] / [CaCO 3 ] = K Since CaCO 3 is solid, it can be treated as constant, K s, then Since CaCO 3 is solid, it can be treated as constant, K s, then [Ca +2 ][CO 3 - ] = KK s = K sp = 5  10 -9 @ 25  C [Ca +2 ][CO 3 - ] = KK s = K sp = 5  10 -9 @ 25  C K sp = solubility constant K sp = solubility constant If [Ca +2 ][CO 3 - ] < K sp, the solution is undersaturated If [Ca +2 ][CO 3 - ] < K sp, the solution is undersaturated If [Ca +2 ][CO 3 - ] > K sp, the solution is supersaturated If [Ca +2 ][CO 3 - ] > K sp, the solution is supersaturated

10. Shift of Equilibria How to shift equilibria How to shift equilibria Produce insoluble products Produce insoluble products Produce gaseous products Produce gaseous products Produce weakly ionized products Produce weakly ionized products Produce oxidation-reduction reaction Produce oxidation-reduction reaction Examples of Equilibria Shift Examples of Equilibria Shift Ca +2 + 2HCO 3 - + Ca(OH) 2  2CaCO 3  + 2CO 2 Ca +2 + 2HCO 3 - + Ca(OH) 2  2CaCO 3  + 2CO 2 3Cl 2 + 2NH 3  N 2  + 6H + + 6Cl - 3Cl 2 + 2NH 3  N 2  + 6H + + 6Cl - 2H + + SO 4 -2 + 2Na + + 2OH -  2H 2 O + 2Na + + SO 4 -2 2H + + SO 4 -2 + 2Na + + 2OH -  2H 2 O + 2Na + + SO 4 -2 5Cl 2 + 2CN - + 8OH -  10Cl - + 2CO 2 + N 2  + 4H 2 O 5Cl 2 + 2CN - + 8OH -  10Cl - + 2CO 2 + N 2  + 4H 2 O

11. pH and Alkalinity pH = log (1 / [H + ]) pH = log (1 / [H + ]) What is alkalinity? What is alkalinity? Is the capacity of the water to neutralize acids without significant change in the pH value Is the capacity of the water to neutralize acids without significant change in the pH value How is alkalinity determined? How is alkalinity determined? Titrating the water with standardized sulfuric acid solution (known normality, usually 0.02N) Titrating the water with standardized sulfuric acid solution (known normality, usually 0.02N) What causes alkalinity? What causes alkalinity? Bicarbonate (HCO 3 - ) Bicarbonate (HCO 3 - ) Carbonate (CO 3 -2 ) Carbonate (CO 3 -2 ) Hydroxyl ions (OH - ) Hydroxyl ions (OH - )

12. Buffers Buffers are substances that offer resistance to a pH change Buffers are substances that offer resistance to a pH change The main buffering system in water and wastewater is the bicarbonate-carbonate system The main buffering system in water and wastewater is the bicarbonate-carbonate system

13. Physical Chemistry Chemical Kinetics Chemical Kinetics Gas Laws Gas Laws Colloidal Dispersions Colloidal Dispersions

14. Chemical Kinetics Zero-order Reactions Zero-order Reactions First-order Reactions First-order Reactions Second-order Reactions Second-order Reactions

15. Zero-Order Reactions The rate is independent of the concentration of the reactant or product The rate is independent of the concentration of the reactant or product The change in concentration of the reactants with time is linear (-dC/dt = k = -r) The change in concentration of the reactants with time is linear (-dC/dt = k = -r) Rearrange and integrate between C 0 to C and t 0 to t Rearrange and integrate between C 0 to C and t 0 to t C-C 0 = -kt OR C = C 0 - kt C-C 0 = -kt OR C = C 0 - kt The equation represents a linear relationship between C and t (y = b + mx) The equation represents a linear relationship between C and t (y = b + mx)

17. First-Order Reactions The rate is proportional to the concentration of a single reactant The rate is proportional to the concentration of a single reactant Change of the reactant with time can be represented by: Change of the reactant with time can be represented by: (-dC/dt) = kC = -r (-dC/dt) = kC = -r Rearrange and integrate to get: Rearrange and integrate to get: ln C = ln C 0 – kt (this is a linear equation) ln C = ln C 0 – kt (this is a linear equation) OR can be written in the form (C/C 0 ) = e -kt OR can be written in the form (C/C 0 ) = e -kt

19. Second-Order Reactions The rate is proportional to the second power of a single reactant The rate is proportional to the second power of a single reactant Change of the reactant with time can be represented by: Change of the reactant with time can be represented by: (-dC/dt) = kC 2 = -r (-dC/dt) = kC 2 = -r Rearrange and integrate to get: Rearrange and integrate to get: 1/C = 1/ C 0 + kt (this is a linear equation) 1/C = 1/ C 0 + kt (this is a linear equation)

21. Effect of Temperature on Reaction Rate Increase in temperature can increase the reaction rate (mostly) Increase in temperature can increase the reaction rate (mostly) Arrhenius derived the following relationship that relates temperature to reaction-rate constant Arrhenius derived the following relationship that relates temperature to reaction-rate constant k 2 = k 1  (t2-t1) (  is the temperature coefficient) k 2 = k 1  (t2-t1) (  is the temperature coefficient) A common value of  is 1.072 A common value of  is 1.072

22. Gas Laws General Gas Law General Gas Law Dalton’s law Dalton’s law Henry’s Law Henry’s Law

23. General Gas Law Is the relationship between pressure, volume, and temperature of a gas at two different conditions. The law states that: Is the relationship between pressure, volume, and temperature of a gas at two different conditions. The law states that: (P 1 V 1 /T 1 ) = (P 2 V 2 /T 2 ) (P 1 V 1 /T 1 ) = (P 2 V 2 /T 2 ) P is the pressure, V is the volume, and T is the absolute temperature in Calvin. P is the pressure, V is the volume, and T is the absolute temperature in Calvin.

24. Dalton’s law In a mixture of gases, each gas exerts a pressure independent of others and the partial pressure of each gas is proportional to the percent by volume of that gas in the mixture. In a mixture of gases, each gas exerts a pressure independent of others and the partial pressure of each gas is proportional to the percent by volume of that gas in the mixture. The partial pressure of each gas is equal to the pressure the gas would exert if it were the sole occupant of the volume available to the mixture. The partial pressure of each gas is equal to the pressure the gas would exert if it were the sole occupant of the volume available to the mixture.

25. Henry’s Law The weight of any gas that would dissolve in a given volume of a liquid, at a constant temperature, is directly proportional to the pressure the gas exerts above the liquid. So The weight of any gas that would dissolve in a given volume of a liquid, at a constant temperature, is directly proportional to the pressure the gas exerts above the liquid. So C s = H p g C s = H p g C s is the concentration of the gas dissolved in the liquid at equilibrium C s is the concentration of the gas dissolved in the liquid at equilibrium H is Henry’s law constant for the gas at the given temperature H is Henry’s law constant for the gas at the given temperature p g is the partial pressure of the gas above the liquid p g is the partial pressure of the gas above the liquid

26. Applications in Environmental Engineering Aeration Aeration The rate of solution of oxygen is proportional to the difference between equilibrium concentration as given by Henry’s Law and the actual concentration in the liquid The rate of solution of oxygen is proportional to the difference between equilibrium concentration as given by Henry’s Law and the actual concentration in the liquid (dC/dt)  (C s – C a ) (dC/dt)  (C s – C a ) Stripping Stripping since C a is greater than C s since C a is greater than C s (dC/dt)  (C a – C s ) (dC/dt)  (C a – C s )

27. Colloidal Dispersions Definition A system in which particles of colloidal size of any nature (e.g. solid, liquid or gas) are dispersed in a continuous phase of a different composition (or state). The name dispersed phase for the particles should be used only if they have essentially the properties of a bulk phase of the same composition.

30. Size and Examples of Colloids Substance consisting of particles that, although too tiny to be seen with the unaided eye (typically 1 nanometer to 10 micrometers), are substantially larger than atoms and ordinary molecules and that are dispersed in a continuous phase. Both the dispersed phase and the continuous phase may be solid, liquid, or gas; examples include suspensions, aerosols, smokes, emulsions, gels, sols, pastes, and foams. Colloids are often classified as reversible or irreversible, depending on whether their components can be separated. Dyes, detergents, polymers, proteins, and many other important substances exhibit colloidal behavior.

31. Classification of Colloids One way of classifying colloids is to group them according to the phase (solid, liquid, or gas) of the dispersed substance and of the medium of dispersion. A gas may be dispersed in a liquid to form a foam (e.g., shaving lather or beaten egg white) or in a solid to form a solid foam (e.g., styrofoam or marshmallow). A liquid may be dispersed in a gas to form an aerosol (e.g., fog or aerosol spray), in another liquid to form an emulsion (e.g., homogenized milk or mayonnaise), or in a solid to form a gel (e.g., jellies or cheese). A solid may be dispersed in a gas to form a solid aerosol (e.g., dust or smoke in air), in a liquid to form a sol (e.g., ink or muddy water), or in a solid to form a solid sol (e.g., certain alloys).

32. Formation of Colloids There are two basic methods of forming a colloid: reduction of larger particles to colloidal size, and condensation of smaller particles (e.g., molecules) into colloidal particles. Some substances (e.g., gelatin or glue) are easily dispersed (in the proper solvent) to form a colloid; this spontaneous dispersion is called peptization. A metal can be dispersed by evaporating it in an electric arc; if the electrodes are immersed in water, colloidal particles of the metal form as the metal vapor cools. A solid (e.g., paint pigment) can be reduced to colloidal particles in a colloid mill, a mechanical device that uses a shearing force to break apart the larger particles. An emulsion is often prepared by homogenization, usually with the addition of an emulsifying agent. The above methods involve breaking down a larger substance into colloidal particles. Condensation of smaller particles to form a colloid usually involves chemical reactions— typically displacement, hydrolysis, or oxidation and reduction.

33. Properties of Colloids One property of colloid systems that distinguishes them from true solutions is that colloidal particles scatter light. If a beam of light, such as that from a flashlight, passes through a colloid, the light is reflected (scattered) by the colloidal particles and the path of the light can therefore be observed. When a beam of light passes through a true solution (e.g., salt in water) there is so little scattering of the light that the path of the light cannot be seen and the small amount of scattered light cannot be detected except by very sensitive instruments. The scattering of light by colloids, known as the Tyndall effect, was first explained by the British physicist John Tyndall. When an ultramicroscope (see microscope) is used to examine a colloid, the colloidal particles appear as tiny points of light in constant motion; this motion, called Brownian movement, helps keep the particles in suspension. Absorption is another characteristic of colloids, since the finely divided colloidal particles have a large surface area exposed. The presence of colloidal particles has little effect on the colligative properties (boiling point, freezing point, etc.) of a solution.

34. Properties of Colloids The particles of a colloid selectively absorb ions and acquire an electric charge. All of the particles of a given colloid take on the same charge (either positive or negative) and thus are repelled by one another. If an electric potential is applied to a colloid, the charged colloidal particles move toward the oppositely charged electrode; this migration is called electrophoresis. If the charge on the particles is neutralized, they may precipitate out of the suspension. A colloid may be precipitated by adding another colloid with oppositely charged particles; the particles are attracted to one another, coagulate, and precipitate out. Addition of soluble ions may precipitate a colloid; the ions in seawater precipitate the colloidal silt dispersed in river water, forming a delta. A method developed by F. G. Cottrell reduces air pollution by removing colloidal particles (e.g., smoke, dust, and fly ash) from exhaust gases with electric precipitators. Particles in a lyophobic system are readily coagulated and precipitated, and the system cannot easily be restored to its colloidal state. A lyophilic colloid does not readily precipitate and can usually be restored by the addition of solvent.

35. Interaction between colloid particles The following forces play an important role in the interaction of colloid particles: Excluded Volume Repulsion: This refers to the impossibility of any overlap between hard particles. Excluded Volume Repulsion: This refers to the impossibility of any overlap between hard particles. Electrostatic interaction: Colloidal particles often carry an electrical charge and therefore attract or repel each other. The charge of both the continuous and the dispersed phase, as well as the mobility of the phases are factors affecting this interaction. Electrostatic interaction: Colloidal particles often carry an electrical charge and therefore attract or repel each other. The charge of both the continuous and the dispersed phase, as well as the mobility of the phases are factors affecting this interaction. van der Waals forces: This interaction is due to induced dipole-dipole interaction. Even if the particles don't have a permanent dipole, fluctuations of the electron density gives rise to a temporary dipole, meaning that van der Waals forces are always present, although possibly at a much lower magnitude than others. van der Waals forces: This interaction is due to induced dipole-dipole interaction. Even if the particles don't have a permanent dipole, fluctuations of the electron density gives rise to a temporary dipole, meaning that van der Waals forces are always present, although possibly at a much lower magnitude than others. Entropic forces: According to the second law of thermodynamics, a system progresses to a state in which entropy is maximized. This can result in effective forces even between hard spheres. Entropic forces: According to the second law of thermodynamics, a system progresses to a state in which entropy is maximized. This can result in effective forces even between hard spheres. Steric forces between polymer-covered surfaces or in solutions containing non-adsorbing polymer can modulate interparticle forces, producing an additional repulsive steric stabilization force or attractive depletion force between them. Steric forces between polymer-covered surfaces or in solutions containing non-adsorbing polymer can modulate interparticle forces, producing an additional repulsive steric stabilization force or attractive depletion force between them.

36. Stabilization of Colloid Suspensions Stabilization serves to prevent colloids from aggregating. Steric stabilization and electrostatic stabilization are the two main mechanisms for colloid stabilization. Electrostatic stabilization is based on the mutual repulsion of like electrical charges. Different phases generally have different charge affinities, so that a charge double-layer forms at any interface. Small particle sizes lead to enormous surface areas, and this effect is greatly amplified in colloids. In a stable colloid, mass of a dispersed phase is so low that its buoyancy or kinetic energy is too little to overcome the electrostatic repulsion between charged layers of the dispersing phase. The charge on the dispersed particles can be observed by applying an electric field: all particles migrate to the same electrode and therefore must all have the same sign charge.

37. Destabilizing a Colloidal Suspension Unstable colloidal suspensions form flocs as the particles aggregate due to inter-particle attractions. This can be accomplished by a number of different methods: Removal of the electrostatic barrier that prevents aggregation of the particles. This can be accomplished by the addition of salt to a suspension or changing the pH of a suspension to effectively neutralize or "screen" the surface charge of the particles in suspension. This removes the repulsive forces that keep colloidal particles separate and allows for coagulation due to van der Waals forces. Removal of the electrostatic barrier that prevents aggregation of the particles. This can be accomplished by the addition of salt to a suspension or changing the pH of a suspension to effectively neutralize or "screen" the surface charge of the particles in suspension. This removes the repulsive forces that keep colloidal particles separate and allows for coagulation due to van der Waals forces. Addition of a charged polymer flocculant. Polymer flocculants can bridge individual colloidal particles by attractive electrostatic interactions. For example, negatively charged colloidal silica particles can be flocculated by the addition of a positively charged polymer. Addition of a charged polymer flocculant. Polymer flocculants can bridge individual colloidal particles by attractive electrostatic interactions. For example, negatively charged colloidal silica particles can be flocculated by the addition of a positively charged polymer. Addition of nonadsorbed polymers called depletants that cause aggregation due to entropic effects. Addition of nonadsorbed polymers called depletants that cause aggregation due to entropic effects.